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MTH120_Chapter2

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MTH120_Chapter2

1. 1. 2- 1 Chapter Two Describing Data: Frequency Distributions and Graphic Presentation GOALS When you have completed this chapter, you will be able to:ONEOrganize data into a frequency distribution. TWO Portray a frequency distribution in a histogram, frequency polygon, andcumulative frequency polygon.THREEDevelop a stem-and-leaf display. FOUR Present data using such graphic techniques as line charts, bar charts, and pie charts.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
2. 2. 2- 2 Frequency Distribution A Frequency distribution is a grouping of data into mutually exclusive categories showing the number of observations in each class.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3. 3. 2- 3 Construction of a Frequency Distribution q u e s t io n t o c o lle c t d a t a o r g a n iz e d a t a p re s e n t d a ta d ra w b e a d re s s e d (ra w d a ta ) (g ra p h ) c o n c lu s io n fr e q u e n c y d is t r ib u t io nMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
4. 4. 2- 4 Frequency Distribution Class midpoint: A point that divides a class into two equal parts. This is the average of the upper and lower class limits. Class frequency: The number of observations in each class. Class interval: The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
5. 5. 2- 5 EXAMPLE 1 Dr. Tillman is Dean of the School of Business Socastee University. He wishes prepare to a report showing the number of hours per week students spend studying. He selects a random sample of 30 students and determines the number of hours each student studied last week. 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Organize the data into a frequency distribution.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
6. 6. 2- 6 Example 1 continued There are 30 observations Two raised to the fifth power is 32. Therefore, we should have at least 5 classes. It turns out we will need 6. The range is 23.5 hours, found by 33.8 hours – 10.3 hours. We choose an interval of 5 hours. The lower limit of the first class is 7.5 hours.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
7. 7. 2- 7 EXAMPLE 1 continued Hours studying Frequency, f 7.5 up to 12.5 1 12.5 up to 17.5 12 17.5 up to 22.5 10 22.5 up to 27.5 5 27.5 up to 32.5 1 32.5 up to 37.5 1McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
8. 8. 2- 8 Suggestions on Constructing a Frequency Distribution  The class intervals used in the frequency distribution should be equal. Determine a suggested class interval by using the formula: (Highest value - Lowest value) i= Number of classesMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
9. 9. 2- 9 Suggestions on Constructing a Frequency Distribution Use the computed suggested class interval to construct the frequency distribution. Note: this is a suggested class interval; if the computed class interval is 97, it may be better to use 100. Count the number of values in each class.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
10. 10. 2- 10 Example 1 continued A relative frequency distribution shows the percent of observations in each class.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11. 11. 2- 11Relative Frequency Distribution Hours f Relative Frequency 7.5 up to 12.5 1 1/30=.0333 12.5 up to 17.5 12 12/30=.400 17.5 up to 22.5 10 10/30=.333 22.5 up to 27.5 5 5/30=.1667 27.5 up to 32.5 1 1/30=.0333 32.5 up to 37.5 1 1/30=.0333 TOTAL 30 30/30=1 TMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
12. 12. 2- 12 Stem-and-leaf Displays Stem-and-leaf display: A statistical technique for displaying a set of data. Each numerical value is divided into two parts: the leading digits become the stem and the trailing digits the leaf. Note: an advantage of the stem-and-leaf display over a frequency distribution is we do not lose the identity of each observation.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
13. 13. 2- 13 EXAMPLE 2 Colin achieved the following scores on his twelve accounting quizzes this semester: 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Construct a stem-and-leaf chart.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
14. 14. 2- 14 Example 2 continued stem leaf 6 9 7 89 8 234568 9 126McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
15. 15. 2- 15 Graphic Presentation of a Frequency Distribution The three commonly used graphic forms are histograms, frequency polygons, and a cumulative frequency distribution. A Histogram is a graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
16. 16. 2- 16 Graphic Presentation of a Frequency Distribution A frequency polygon consists of line segments connecting the points formed by the class midpoint and the class frequency. A cumulative frequency distribution is used to determine how many or what proportion of the data values are below or above a certain value.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
17. 17. 2- 17 Histogram for Hours Spent Studying 14 12 Frequency 10 8 6 4 2 0 10 15 20 25 30 35 Hours spent studyingMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
18. 18. 2- 18 Frequency Polygon for Hours Spent Studying 14 12 10 Frequency 8 6 4 2 0 10 15 20 25 30 35 Hours spent studyingMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
19. 19. 2- 19 Cumulative Frequency Distribution For Hours Studying 35 30 25 20 Frequency 15 10 5 0 10 15 20 25 30 35 Hours Spent StudyingMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
20. 20. 2- 20 Bar Chart A bar chart can be used to depict any of the levels of measurement (nominal, ordinal, interval, or ratio).McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
21. 21. 2- 21 Example3 EXAMPLE 3: Construct a bar chart for the number of unemployed per 100,000 population for selected cities during 2001 City Number of unemployed per 100,000 population Atlanta, GA 7300 Boston, MA 5400 Chicago, IL 6700 Los Angeles, CA 8900 New York, NY 8200 Washington, D.C. 8900McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
22. 22. 2- 22 Bar Chart for the Unemployment Data 10000 8900 8900 # unemployed/100,000 8200 8000 7300 6700 5400 Atlanta 6000 Boston 4000 Chicago Los Angeles 2000 New York 0 Washington 1 2 3 4 5 6 CitiesMcGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
23. 23. 2- 23 Pie Chart A pie chart is useful for displaying a relative frequency distribution. A circle is divided proportionally to the relative frequency and portions of the circle are allocated for the different groups.McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24. 24. 2- 24 EXAMPLE 4 continued EXAMPLE 4: A sample of 200 runners were asked to indicate their favorite type of running shoe. Draw a pie chart based on the following information. Type of shoe # of runners Nike 92 Adidas 49 Reebok 37 Asics 13 Other 9McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.